diff --git a/sdk/core/core-http/src/fetchHttpClient.ts b/sdk/core/core-http/src/fetchHttpClient.ts
index 203489f08edc..59cce702e44b 100644
--- a/sdk/core/core-http/src/fetchHttpClient.ts
+++ b/sdk/core/core-http/src/fetchHttpClient.ts
@@ -213,7 +213,10 @@ export abstract class FetchHttpClient implements HttpClient {
         }
         let downloadStreamDone = Promise.resolve();
         if (isReadableStream(operationResponse?.readableStreamBody)) {
-          downloadStreamDone = isStreamComplete(operationResponse!.readableStreamBody);
+          downloadStreamDone = isStreamComplete(
+            operationResponse!.readableStreamBody,
+            abortController
+          );
         }
 
         Promise.all([uploadStreamDone, downloadStreamDone])
@@ -237,11 +240,14 @@ function isReadableStream(body: any): body is Readable {
   return body && typeof body.pipe === "function";
 }
 
-function isStreamComplete(stream: Readable): Promise<void> {
+function isStreamComplete(stream: Readable, aborter?: AbortController): Promise<void> {
   return new Promise((resolve) => {
-    stream.on("close", resolve);
-    stream.on("end", resolve);
-    stream.on("error", resolve);
+    stream.once("close", () => {
+      aborter?.abort();
+      resolve();
+    });
+    stream.once("end", resolve);
+    stream.once("error", resolve);
   });
 }
 
diff --git a/sdk/core/core-http/test/defaultHttpClientTests.node.ts b/sdk/core/core-http/test/defaultHttpClientTests.node.ts
index f312e53e808d..ae635d825982 100644
--- a/sdk/core/core-http/test/defaultHttpClientTests.node.ts
+++ b/sdk/core/core-http/test/defaultHttpClientTests.node.ts
@@ -12,10 +12,11 @@ import { createReadStream, ReadStream } from "fs";
 import { DefaultHttpClient } from "../src/defaultHttpClient";
 import { WebResource, TransferProgressEvent } from "../src/webResource";
 import { getHttpMock, HttpMockFacade } from "./mockHttp";
-import { PassThrough } from "stream";
+import { PassThrough, Readable } from "stream";
 import { ReportTransform, CommonResponse } from "../src/fetchHttpClient";
 import { CompositeMapper, Serializer } from "../src/serializer";
 import { OperationSpec } from "../src/operationSpec";
+import { AbortController } from "@azure/abort-controller";
 
 describe("defaultHttpClient (node)", function() {
   let httpMock: HttpMockFacade;
@@ -427,6 +428,51 @@ describe("defaultHttpClient (node)", function() {
       requestInit2.agent.proxyOptions.proxyAuth
     );
   });
+
+  it("should abort connection when download stream is closed", async function() {
+    const payload = new PassThrough();
+    const b = new PassThrough();
+    b.pipe(payload, { end: false });
+    b.write("hello");
+    const response = {
+      status: 200,
+      headers: [],
+      body: payload
+    };
+
+    let signal: AbortSignal | undefined;
+    const client = new DefaultHttpClient();
+    sinon.stub(client, "fetch").callsFake(async (_input, init) => {
+      assert.ok(init, "expecting valid request initialization");
+      signal = init!.signal;
+      return (response as unknown) as CommonResponse;
+    });
+
+    const ac = new AbortController();
+    const request = new WebResource(
+      "http://myhost/bigdownload",
+      "GET",
+      undefined,
+      undefined,
+      undefined,
+      true
+    );
+    request.abortSignal = ac.signal;
+    const promise = client.sendRequest(request);
+
+    const res = await promise;
+    assert.ok(res.readableStreamBody, "Expecting valid download stream");
+
+    assert.ok(signal, "Expecting valid signal");
+    const abortFiredPromise = new Promise<void>((resolve) => {
+      signal!.onabort = () => {
+        resolve();
+      };
+    });
+    const stream: Readable = res.readableStreamBody as any;
+    stream.destroy();
+    await abortFiredPromise; // 'abort' event fired
+  });
 });
 
 describe("ReportTransform", function() {